{
  "id": "1204.2981",
  "version": "v1",
  "published": "2012-04-13T13:11:15.000Z",
  "updated": "2012-04-13T13:11:15.000Z",
  "title": "A connection between the bipartite complements of line graphs and the line graphs with two positive eigenvalues",
  "authors": [
    "Lee Gumbrell"
  ],
  "comment": "4 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "In 1974 Cvetkovi\\'c and Simi\\'c showed which graphs $G$ are the bipartite complements of line graphs. In 2002 Borovi\\'canin showed which line graphs $L(H)$ have third largest eigenvalue $\\lambda_3\\leq0$. Our first observation is that two of the graphs Borovi\\'canin found are the complements of two of the graphs found by Cvetkovi\\'c and Simi\\'c. Using the Courant-Weyl inequalities we show why this is and reprove the result of Borovi\\'canin, highlighting some features of the graphs found by both.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-13T13:11:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "line graphs",
      "bipartite complements",
      "positive eigenvalues",
      "connection",
      "third largest eigenvalue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.2981G"
    }
  }
}